Our story begins on a test server hosting a couple hundred databases. Over time, the server kept getting slower and slower when trying to navigate in SSMS. Query windows would take too much time to load, logging in would lag a bit, etc. When investigating with sp_Blitz, I found that the server had been experiencing Threadpool waits.
There are some cases where increasing thread count is important, especially when you’re working with database mirroring or availability groups. I worked with a customer with thousands of mirrored databases per server. None of the databases were particularly large or heavily-used, so it was on properly-sized hardware. As a result, to prevent the server from falling over due to threadpool waits, we had to scale thread counts to scary-high levels.